Global stability, limit cycles and chaotic behaviors of second order interpolative sigma delta modulators

It is well known that second order lowpass interpolative sigma delta modulators (SDMs) may suffer from instability and limit cycle problems when the magnitudes of the input signals are at large and at intermediate levels, respectively. In order to solve these problems, we propose to replace the second order lowpass interpolative SDMs to a specific class of second order bandpass interpolative SDMs with the natural frequencies of the loop filters very close to zero. The global stability property of this class of second order bandpass interpolative SDMs is characterized and some interesting phenomena are discussed. Besides, conditions for the occurrence of limit cycle and fractal behaviors are also derived, so that these unwanted behaviors will not happen or can be avoided. Moreover, it is found that these bandpass SDMs may exhibit irregular and conical-like chaotic patterns on the phase plane. By utilizing these chaotic behaviors, these bandpass SDMs can achieve higher signal-to-noise ratio (SNR) and tonal suppression than those of the original lowpass SDMs

Nonlinear behaviors of bandpass sigma delta modulators with stable system matrices

It has been established that a class of bandpass sigma delta modulators (SDMs) may exhibit state space dynamics which are represented by elliptical or fractal patterns confined within trapezoidal regions when the system matrices are marginally stable. In this paper, it is found that fractal patterns may also be exhibited in the phase plane when the system matrices are strictly stable. This occurs when the sets of initial conditions corresponding to convergent or limit cycle behavior do not cover the whole phase plane. Based on the derived analytical results, some interesting results are found. If the bandpass SDM exhibits periodic output, then the period of the symbolic sequence must equal the limiting period of the state space variables. Second, if the state vector converges to some fixed points on the phase portrait, these fixed points do not depend directly on the initial conditions

NEW LIGHT ON TAIWAN HIGHLAND PREHISTORY

Compared to the Western Plains and the East Coast, archaeological research in the central Taiwan Highlands has been very limited. In recent decades, not only most CRM archaeology but also the most active archaeological excavations in Taiwan have been conducted in the lowlands, giving results which have greatly enriched our understanding of Taiwanese prehistory. Nevertheless, archaeological study in the mountainous areas, nowadays mostly inhabited by Austronesian-speaking Formosan people, lapsed after the Japanese colonial period (18951945). Although some excavation and survey projects have been conducted in the highlands since the 1980s (e.g. Chiu and Gao 1988; Tsang and Chang 1995, 1996; Liu and Ho 1998), the limited literature is mostly based on the work of Japanese archaeologists and ethnologists undertaken over sixty years ago. To have a more comprehensive discussion about prehistoric island-wide population movements and cultural interactions, further archaeological work in the interior mountains of Taiwan is necessary. The National Museum of Natural Science in Taichung commissioned a digital museum project on Tsou culture in 2001 and 2002. During this time, the authors conducted archaeological fieldwork in the Ali Shan area of central Taiwan (Fig. 1). Abundant sites and remains were researched during this project and the results are presented here

Nonlinear behaviors of bandpass sigma delta modulators with stable system matrices

It has been established that a class of bandpass sigma-delta modulators may exhibit state space dynamics which are represented by elliptical or fractal patterns confined within trapezoidal regions when the system matrices are marginally stable. In this brief, it is found that fractal or irregular chaotic patterns may also be exhibited in the phase plane when the system matrices are strictly stabl

Normalized histogram of the state variable of first-order digital filters with two’s complement arithmetic

In this letter, the normalized histogram of the state variable of first-order digital filters with two’s complement arithmetic is investigated. When the pole of the digital filter is between 1 and 2, it is found that the possibility of occurrence of the state variable in certain region is close to zero no matter what the initial condition is. Some analytic results are given to account for this phenomenon

Computer-aided design and optimization of high-efficiency LLC series resonant converter

High conversion efficiency is desired in switch mode power supply converters. Computer-aided design optimization is emerging as a promising way to design power converters. In this work a systematic optimization procedure is proposed to optimize LLC series resonant converter full load efficiency. A mode solver technique is proposed to handle LLC converter steady-state solutions. The mode solver utilizes numerical nonlinear programming techniques to solve LLC-state equations and determine operation mode. Loss models are provided to calculate total component losses using the current and voltage information derived from the mode solver. The calculated efficiency serves as the objective function to optimize the converter efficiency. A prototype 300-W 400-V to 12-V LLC converter is built using the optimization results. Details of design variables, boundaries, equality/inequality constraints, and loss distributions are given. An experimental full-load efficiency of 97.07 is achieved compared to a calculated 97.4 efficiency. The proposed optimization procedure is an effective way to design high-efficiency LLC converters. © 1986-2012 IEEE.published_or_final_versio

Occurence of elliptical fractal patterns in multi-bit bandpass sigma delta modulators

It has been established that the class of bandpass sigma delta modulators (SDMs) with single bit quantizers could exhibit state space dynamics represented by elliptic or fractal patterns confined within trapezoidal regions. In this letter, we find that elliptical fractal patterns may also occur in bandpass SDMs with multibit quantizers, even for the case when the saturation regions of the multibit quantizers are not activated and a large number of bits are used for the implementation of the quantizers. Moreover, the fractal pattern may occur for low bit quantizers, and the visual appearance of the phase portraits between the infinite state machine and the finite state machine with high bit quantizers is different. These phenomena are different from those previously reported for the digital filter with two’s complement arithmetic. Furthermore, some interesting phenomena are found. A bit change of the quantizer can result in a dramatic change in the fractal patterns. When the trajectories of the corresponding linear systems converge to a fixed point, the regions of the elliptical fractal patterns diminish in size as the number of bits of the quantizers increases

Quality assessment on Polygoni Multiflori Caulis using HPLC/UV/MS combined with principle component analysis

BACKGROUND: Polygoni Multiflori Caulis, the dried caulis of Polygonum multiflorum Thunb., is one of the commonly used traditional Chinese medicines having antioxidant, anti-obesity, anti-inflammatory and antibacterial effects. Polygoni Multiflori Caulis used clinically or circulated on market have great differences in their diameters. However, to the best of our knowledge, no study has been reported on the qualities of Polygoni Multiflori Caulis with different diameters. RESULTS: Systematic HPLC/UV/MS chromatographic fingerprinting and quantitative analytical methods combined with principal component analysis were developed and applied to analyze different Polygoni Multiflori Caulis samples. The contents of 2,3,5,4′-tetrahydroxystilbene-2-O-β-D-glucoside, the chemical marker for quality control on Polygoni Multiflori Caulis specified in Chinese Pharmacopoeia (2010 edition), were found to have surprising relevance with the samples’ diameters for the first time. CONCLUSION: The finding provides a scientific basis for collecting Polygoni Multiflori Caulis in the best time. Moreover, the diameter can be used as the criterion for quality control on Polygoni Multiflori Caulis as a preliminary step in the future. In addition, scores plot obtained from principal component analysis shows the obvious differences between unqualified Polygoni Multiflori Caulis samples and qualified ones visually, which can be used to single out the unqualified ones with qualified ones efficiently and immediately

Fucosyltransferase 1 and 2 play pivotal roles in breast cancer cells.

FUT1 and FUT2 encode alpha 1, 2-fucosyltransferases which catalyze the addition of alpha 1, 2-linked fucose to glycans. Glycan products of FUT1 and FUT2, such as Globo H and Lewis Y, are highly expressed on malignant tissues, including breast cancer. Herein, we investigated the roles of FUT1 and FUT2 in breast cancer. Silencing of FUT1 or FUT2 by shRNAs inhibited cell proliferation in vitro and tumorigenicity in mice. This was associated with diminished properties of cancer stem cell (CSC), including mammosphere formation and CSC marker both in vitro and in xenografts. Silencing of FUT2, but not FUT1, significantly changed the cuboidal morphology to dense clusters of small and round cells with reduced adhesion to polystyrene and extracellular matrix, including laminin, fibronectin and collagen. Silencing of FUT1 or FUT2 suppressed cell migration in wound healing assay, whereas FUT1 and FUT2 overexpression increased cell migration and invasion in vitro and metastasis of breast cancer in vivo. A decrease in mesenchymal like markers such as fibronectin, vimentin, and twist, along with increased epithelial like marker, E-cadherin, was observed upon FUT1/2 knockdown, while the opposite was noted by overexpression of FUT1 or FUT2. As expected, FUT1 or FUT2 knockdown reduced Globo H, whereas FUT1 or FUT2 overexpression showed contrary effects. Exogenous addition of Globo H-ceramide reversed the suppression of cell migration by FUT1 knockdown but not the inhibition of cell adhesion by FUT2 silencing, suggesting that at least part of the effects of FUT1/2 knockdown were mediated by Globo H. Our results imply that FUT1 and FUT2 play important roles in regulating growth, adhesion, migration and CSC properties of breast cancer, and may serve as therapeutic targets for breast cancer